Answer:
The answer is B complimentary
Explanation:
Answer:
a) (0, -33, 12)
b) area of the triangle : 17.55 units of area
Explanation:
<h2>
a) </h2>
We know that the cross product of linearly independent vectors
and
gives us a nonzero, orthogonal to both, vector. So, if we can find two linearly independent vectors on the plane through the points P, Q, and R, we can use the cross product to obtain the answer to point a.
Luckily for us, we know that vectors
and
are living in the plane through the points P, Q, and R, and are linearly independent.
We know that they are linearly independent, cause to have one, and only one, plane through points P Q and R, this points must be linearly independent (as the dimension of a plane subspace is 3).
If they weren't linearly independent, we will obtain vector zero as the result of the cross product.
So, for our problem:







<h2>B)</h2>
We know that
and
are two sides of the triangle, and we also know that we can use the magnitude of the cross product to find the area of the triangle:

so:




You can mark, lift and clean a ball on the green, but it's a violation to do so when another ball is in motion, as your ball might influence the outcome of that stroke. You can also mark and clean your ball in some instances when it's off the green: cleaning it, for example, just to the point where you can identify it.
I would say that this is the first law of thermodynamics.